Answer:
30
Step-by-step explanation:
Average rate of change=Δf(x)/Δx = [f(x2)-f(x1]/[x2-x1]
Δf(x)/Δx = [f(5)-f(1]/[5-1]
f(5)=5³-5=120
f(1)=1³-1=0
Δf(x)/Δx = [120-0]/[5-1]=120/4=30
9514 1404 393
Answer:
5√5
Step-by-step explanation:
Use the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((-7-(-2))² +(-7-3)²) = √((-5)² +(-10)²) = √(25 +100)
d = √125 = √(25·5)
d = 5√5 . . . . distance between the points
Answer:
Hola que hace
:I
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
The line intersects each parabola in one point, so is tangent to both.
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For the first parabola, the point of intersection is ...
y^2 = 4(-y-1)
y^2 +4y +4 = 0
(y+2)^2 = 0
y = -2 . . . . . . . . one solution only
x = -(-2)-1 = 1
The point of intersection is (1, -2).
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For the second parabola, the equation is the same, but with x and y interchanged:
x^2 = 4(-x-1)
(x +2)^2 = 0
x = -2, y = 1 . . . . . one point of intersection only
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If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.
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Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.